Energy Fluxes due to the Surface and Internal Tides in Knight Inlet, British Columbia

Michael W. Stacey Department of Physics, Royal Military College of Canada, Kingston, Ontario, Canada

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S. Pond Department of Earth and Ocean Sciences, The University of British Columbia, Vancouver, British Columbia, Canada

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Abstract

A laterally integrated (two dimensional) nonlinear numerical model is used to examine the flux of M2 tidal energy in Knight Inlet. The simulated flux of tidal energy into the inlet is somewhat smaller than that estimated using the change in phase of the M2 tidal height along the inlet, a method that does not account for the effect of the internal tide on the surface elevation. The simulated energy flux into the inlet is close to the energy flux of the internal tide away from the sill determined from observations using an acoustic Doppler current profiler (ADCP). The net flux due to the internal tide is significantly less than (<1/2 of) the rate at which energy is removed from the surface tide. Earlier linear models of the internal tide produced energy fluxes that agreed with those estimated from the phase change of the tidal height but were larger than the fluxes that could be found in the observations. The reason for this discrepancy is not that these simple models neglected nonlinear effects, but rather that they did not take reflections of the internal tide into account. Also, the simulated flux of energy into the inlet less the net flux of internal tidal energy away from the sill is about equal to the simulated dissipation within 2 km on either side of the sill. The simulated net flux of internal tidal energy away from the sill is in agreement with the flux determined from the ADCP observations on the downinlet side of the sill, but not on the upinlet side of the sill. A possible explanation is that only the first internal mode (which is surface intensified) was important on the downinlet side but the first three internal modes were important on the upinlet side. The flux calculation using the ADCP observations took variations in the inlet width into account but did not take depth variations into account; thus, the reflection coefficients of the second and third modes may have been underestimated.

Corresponding author address: Dr. Michael W. Stacey, Department of Physics, Royal Military College of Canada, P.O. Box 17000, Station Forces, Kingston, ON K7K 7B4, Canada. Email: stacey-m@rmc.ca

Abstract

A laterally integrated (two dimensional) nonlinear numerical model is used to examine the flux of M2 tidal energy in Knight Inlet. The simulated flux of tidal energy into the inlet is somewhat smaller than that estimated using the change in phase of the M2 tidal height along the inlet, a method that does not account for the effect of the internal tide on the surface elevation. The simulated energy flux into the inlet is close to the energy flux of the internal tide away from the sill determined from observations using an acoustic Doppler current profiler (ADCP). The net flux due to the internal tide is significantly less than (<1/2 of) the rate at which energy is removed from the surface tide. Earlier linear models of the internal tide produced energy fluxes that agreed with those estimated from the phase change of the tidal height but were larger than the fluxes that could be found in the observations. The reason for this discrepancy is not that these simple models neglected nonlinear effects, but rather that they did not take reflections of the internal tide into account. Also, the simulated flux of energy into the inlet less the net flux of internal tidal energy away from the sill is about equal to the simulated dissipation within 2 km on either side of the sill. The simulated net flux of internal tidal energy away from the sill is in agreement with the flux determined from the ADCP observations on the downinlet side of the sill, but not on the upinlet side of the sill. A possible explanation is that only the first internal mode (which is surface intensified) was important on the downinlet side but the first three internal modes were important on the upinlet side. The flux calculation using the ADCP observations took variations in the inlet width into account but did not take depth variations into account; thus, the reflection coefficients of the second and third modes may have been underestimated.

Corresponding author address: Dr. Michael W. Stacey, Department of Physics, Royal Military College of Canada, P.O. Box 17000, Station Forces, Kingston, ON K7K 7B4, Canada. Email: stacey-m@rmc.ca

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